Exploring the legacy of the rationalist Rishonim (medieval Torah scholars), and various other notes, by Rabbi Dr. Natan Slifkin, director of The Biblical Museum of Natural History in Beit Shemesh

Thursday, March 14, 2019

Pi and Rambam

Today, March 14th, is Pi Day (3.14). And pi has been yet another of the battlefronts in the Rationalism/Mysticism Wars.

Rambam (in his commentary to Eruvin 1:5) explicitly describes
pi as being an irrational number (i.e. a number that cannot be accurately expressed
by a fraction).
Rabbi Moshe Meiselman, in Torah, Chazal and Sciencep.
155, claims that
Rambam "was not merely repeating an accepted piece of information, since
this fact was as of yet unknown to the rest of the world." Rabbi
Meiselman further claims that Rambam deduced this from the Talmud (positing a very strange inference that Rambam derived this from Chazal approximating Pi as three rather than using a
fraction, which he claims means that they knew that Pi could not be accurately expressed as a fraction). As such, Rabbi Meiselman presents this as evidence that
Rambam, and in turn Chazal, possessed wisdom that was ahead of their
time, and was somehow derived from the Torah or some other such
supernatural source.

Rabbi Meiselman's claim that has been echoed by others, such as Jonathan Rosenblum and Rabbi Yaakov Menken. They all use it to delegitimize the rationalist approach, claiming that if Rambam had supernatural knowledge of science, then it's foolish to believe that Chazal (who were even greater) made scientific errors.

However, this claim about Rambam and pi is completely false. Rambam's statement about pi is by no means extraordinary.

Boaz Tsaban and David Garber note that "Various ancient Greek writers, including Hero, Eutocius, and
Simplicius, understand the difficulty
of finding an exact value for the ratio, and seem to realize the
possibility of its being irrational," although they did not say so
definitively. It is thus certainly no surprise that after centuries of
failed efforts to calculate the value precisely, people would conclude that
it is indeed irrational.

The fifth-century Indian mathematician Aryabhata wrote that “Add four to 100, multiply by eight and then add 62,000. By this rule
the circumference of a circle of diameter 20,000 can be approached.” The
15th century commentator Nilakantha Somayaji interprets the
original words as saying that not that is this an
approximation, but that the value is irrational.

Then, at the turn of the ninth century, the Persian mathematician
Muhammad Al-Khwarizmi notes that there are several different methods for
calculating Pi. A marginal note (I am not sure when it was written) observes that "It is an approximation not a proof, and no one stands on the truth of
this, and no one but Allah knows the true circumference of the circle,
as the line is not straight and has no beginning and no end, we merely
attempt to approximate and discover the root, but even the root has no
definition as no one may know its exact value but Allah, and the best of
these approximations that is to multiply the diameter by three and
seventh as it is faster and simpler and only Allah might know it true."

The Muslim scholar Abu al-Rayhan al-Biruni, who lived from 973-1048, was familiar with Aryabhata's works. In The Encyclopedia of the History of
Arabic Science, [Roshdi Rashed ed.], vol. 2, London/New York, 1996,
p. 454), Boris Rosenfeld and Youschkevitch note that al-Biruni described
Pi as irrational. In their discussion of medieval Arabic science, they
further note that "...Arabic mathematicians repeatedly expressed
their belief that the ratio of the length of a circumference to its
diameter was irrational... Subsequent European mathematicians were also
sure that pi is irrationalbut only J. H. Lambert, a native of Alsace, in 1766 succeeded in proving this."

Thus, the irrationality of pi was certainly not "as of
yet unknown to the rest of the world." Just as
the early Greeks seem to have suspected and just as the early Indian and
Muslim scholars were certain, Rambam was likewise certain that pi is
irrational. (As for Chazal, there is absolutely no reason to believe that they knew pi to be irrational, but even if they would have known it, this would be consistent with others in antiquity.)

Rambam was an utter genius. But he wasn't ahead of his time scientifically, and he did not have any supernatural sources of knowledge about science. If someone wants to delude themselves into thinking otherwise, it doesn't really bother me; the only problem is when they use this mistaken view to try to delegitimize those who take an honest, factually-based, rationalist approach. And such delegitimization is also, ironically, the ultimate perversion of Rambam's legacy.

69 comments:

I've pointed this out elsewhere, but to "know" something in mathematics is to possess a proof. Before the proof was available, the writers who conjectured that pi is irrational, but did not definitively state that it is were the most correct. Anyone who thought that they knew pi was irrational, but did not possess a proof were actually more *incorrect* because they did not truly know this and were mistaking a good guess for knowledge. (Probably Rambam knew that he didn't really know that it was irrational and just stated his conjecture emphatically).

No, the ancient Greeks had a full understanding of what a mathematical proof was. The proofs that you learned in Geometry class were the same as the proofs in Euclid. Euclid did make a few errors, but those are minor. This was one of the greatest achievements of the ancient world.

The ancients possessed a proof that the square root of 2 is irrational and they knew that they didn't have a proof that pi was irrational.

Certainly our understanding of mathematical logic and it's limits has improved and we've put more areas of math on solid logical foundations, but the mathematical proofs of the ancient world were completely valid and are still used.

Sorry, but I am confused by this post. The Rambam writes not only that he knew pi to be irrational, but that Chazal knew pi to be irrational, which is why they gave their approximation. So all of your sources from the 4th century and on are irrelevant, as they would not support the idea that pi's irrationality was generally known in the time of Chazal.As a side point, the Rambam is very difficult to understand. Even if Chazal did not know that pi was irrational, they certainly knew that is cannot be expressed with a simple number. This itself would justify the use of an approximation.

Is this seriously starting over again? I feel like I am in a time warp. Sunday was a rehash of the old shafan arguments and today the same re pi.

It is irrelevant whether chazal did or did not know or presume pi to be irrational. All that is needed is there to be a general presumption among the mathematically educated at the time or RMB"M and some time before. This is enough to both justify RMB"M stating it as established fact (without bringing any proof) and assuming that earlier scholars were similarly familiar with this fact / presumption.

Those who are predisposed to magical thinking will find other explanations more tenable. Those who are not won't.

Rambam wasn't a Navi and didn't have access to secret material about Chazal's knowledge. This was a statement by Rambam and not by Chazal. This is beside the fact that Rambam projects lots of things onto Chazal that they probably didn't really think (like near-universal opposition to what the Rambam considered superstition). Giving a poor approximation for Pi is not real evidence that they "knew" it to be irrational (which neither they nor the Rambam knew since they did not have proof).

To answer your question, I think that Rambam was concerned to defend the approximation, especially given that it is a pretty poor approximation. So his answer specifically emphasizes his and their sophistication in knowing that there was no known rational corresponding to pi. So it is probably apologetics.

To DZ: I agree with you.To Yoni: That has nothing to do with the very specific critique of the post I made.To David: 1: It was a statement by the Rambam about what Chazal knew. You are offering a new explanation, specifically that the Rambam did not "know" that Chazal knew pi to be irrational, he just assumed that they did. Could be. 2: Not sure what you mean. He could have just as easily said that Chazal knew that pi cannot be precisely expressed with ease, so they chose an approximation. There was no reason for him to get into the question of if pi is irrational, and if Chazal knew that.3: Irrelevant. Even if you want to continue the editing of the Gemara until the 9th century, the statements about the circumference of a circle are definitely before the 4th.

Actually, I refreshed my memory on what he actually wrote. He just says that this it is a well known fact that pi cannot be calculated exactly and fools think otherwise. He wasn't attributing to himself or Chazal any special knowledge. He quotes the expert geometers as having given the 22/7 approximation.

“Sorry, but I am confused by this post. The Rambam writes not only that he knew pi to be irrational, but that Chazal knew pi to be irrational, which is why they gave their approximation. “

@Yehoshua - It seems to be the confusion is that is not what RNS stated, which was -

“Rabbi Meiselman further claims that Rambam deduced this from the Talmud (positing a very strange inference that Rambam derived this from Chazal approximating Pi as three rather than using a fraction,”

So RNS is claiming that it is RMM (Not RAMBAM) who suggests RAMBAM got his information from Chazal.

@yehoshua - you seem to agree that “the Rambam is very difficult to understand.”

Accordingly the sources after the fourth century are not irrelevant because they shed light on where RAMBAM may have actually gotten further evidence that Pi is indeed irrational.

Jeffrey: There are three separate issues here. 1: Did the Rambam claim that Chazal knew pi to be irrational? 2: Did Chazal in fact know it is irrational? 3: If they knew this, is that evidence of their supernatural knowledge? RMM is claiming yes to all three. I think the third is ridiculous, the second is questionable, and the first seems to be yes. RNS is claiming that even if 1 and 2 are true, one cannot infer 3, because of the host of early citations that pi is irrational. I am merely pointing out that the post-Talmudic citations are relevant only to the Rambam's knowing that pi is irrational, and not to the Rambam's claim that Chazal knew it to be irrational.

The pattern continues: Rashi is an idiot because he's describing a camel's feet even though he probably never saw a camel. The Rambam didn't know PI. The movement to find inaccuracies and unqualified scholarship in the transmitters of the mesorah continues. While I don't consider it a bad thing if Rashi never saw a camel or Rambam didn't know PI - it's the underlying snipping and looking to point out what they didn’t know. HOW ABOUT FOCUS ON WHAT THEY DID KNOW INSTEAD OF POINTING OUT THEIR SUPPOSED inadequacies.

Not knowing something is not an inadequacy. Every generation adds to the general store of knowledge. We are not idiots because we don't know many things that will be known in 100 years. Rambam himself describes Chazal as not necessarily knowing the size of the heavenly bodies because the math was not developed enough at their time.

It is R Meiselman and others like him who think that if Chazal or Rishonim don't know something, that this somehow is offensive. You should address yourself to them.

RNS is pointing out that current authorities are making claims that do not withstand scrutiny. I understand that you don't particularly care for truth, but some people do. As Marc Shapiro has documented, the practice of playing loose with sources has a long tradition in Judaism. That doesn't mean it should continue unopposed.

עפרא לפומיך for putting those terrible words in other people's mouths. Rav Miller zt"l tape 624 is asked if you have to believe that Chazal knew modern science and math. He says you don't have to - if you asked Eliyahu Hanavi to fix the air conditioner and he didn't know how to do it, would that take away from his greatness? That's RIDICULOUS! … ע"ש שהאריך.

(This is Chazal. R Feldman writes that no one holds the Rishonim scientifically infallible.)

The pattern continues: Slifkin is an idiot, Slifkin doesn't know this, focuses only on that, etc. HOW ABOUT FOCUSING ON WHAT HE DOES KNOW, INSTEAD OF POINTING OUT SUPPOSED INADEQUACIES?

On a more serious note, RNS sees a charedi world in which ChaZaL are seen as infallible, and he will therefore work to point out and provide proof that this is not the case. It is no different to other forums where someone is having to constantly 'grow' and build their case, in order to prove it. Here in the uk, for example, commentators have been relentless in stating their case for, or against Brexit. They have been doing it for a long time, providing proof after proof after proof, and so they should if they want to keep their case alive. And in this case, it seems it is important and necessary, because despite all the blog posts, RNSR has not yet managed to convince you.

I have gained a lot and managed to hold onto religious Judaism only because of the repeated blog posts which eventually convinced me that there is a way for me to keep believing, and no, one post or book would not have been enough, so I am happy for RNS to keep it coming, although I don't keep up with all the posts.

May I gently suggest that if you want to focus on what Rashi and Rambam knew, you should spend more time learning their seforim, and less time on this blog. It's for some people, but maybe not for you...

RNS is not pointing out the inadequacies of the Rambam or Rashi. You are sorely missing the point. He is zeroing in on the toxic and harmful claim espoused by a major subset of Judaism that chazal possessed divine wisdom that came down from shamayim and that they knew everything. This creates the perverted notion that all you need is Torah and you're okay, that there is no need for secular education and that you need to box yourself in from the rest of the world and be sheltered under the rabbonim. This not only disregards other forms of wisdom, it completely distorts chazal and the true depth of their teachings, and ultimately turns Judaism into a non-sensical and disconnected way of life.

The only inadequacies RNS is highlighting are those from the ArtScroll publishers (regarding the camel) and Rabbi Meiselman (regarding Pi), not Rambam and Rashi. Your biases blind you.

You guys all missed the point. In theory I can agree to all of these claims regarding chazal and Rishonim. It's the toxic underlying and flippant attitude toward the conveyors of our mesorah that I protest. When we speak of and to great men, a certain etiquette is warranted.

Who are the "conveyors of our mesorah" that you are referring to? R Meiselman or the Rambam/Rashi? If the latter, where is the "flippant attitude" and lack of "etiquette" toward them? If the former, what gives any rabbi grounds to be labeled a "conveyor of our mesorah" that puts them above the rest?

I think we missed the point because you didn't make clear that you worship CHaZaL, and possibly the Rishonim, and consider any discussion that focuses on them as products of their time as being disrespectful.

Modern_Orthodox: Where is the "toxic underlying and flippant attitude"? Where does RNS break "etiquette"? RNS clearly does not subscribe to the charedi view that we must not question what we are told. There are good reasons to wonder if chazal and early rabbis had accurate information at their disposal, and if that information was conveyed properly over the years. Trying to understand is an essential element of Judaism, even if the charedi world would have us believe otherwise. There are ways to question potentially faulty concepts, which RNS does without disparaging the rabbis who originally espoused them. If your only purpose is to comment on every post about how the charedi viewpoint is correct and that RNS is always wrong, maybe you should remember why this blog was created in the first place.

No, you missed the point. The outrageous words that you put into other people's mouth's are inexcusable. Ditto if you're railing against the imagined attitude that people have. Quit with your exaggerated attitude. Reorient yourself with what greatness is. Are you in awe of people much much greater than you who know less science than you. (I am.) Why are you in awe of them? Is it their character, devotion, Torah knowledge, compassion, leadership? Then you make a ק"ו to Chazal & Rishonim. That's all. Because you underappreciate Chazal & Rishonim in those other ways you need to prop them up with scientific infallibility.

This isn't a complaint against Chareidi education if they don't bother others, but that's not the point now. You've been exposed by now to enough information to reconsider which views can be legitimate and respectful. Stop already with your denunciations.

Go review "In Defence" 's comment,"I have gained a lot and managed to hold onto religious Judaism only because of the repeated blog posts which eventually convinced me that there is a way for me to keep believing". And look at zootorah.com/controversy for similar sentiments. And a few people expressed the same sentiments to me personally. But if things went your way they wouldn't believe. You're a monster.

Which means that R Evyasar remains a Gavra Raba despite his ignorance of what R Yitzchak said (and violating R Yitzchak's Halacha). This is ignorance of Torah. Certainly ignorance of science doesn't stop anyone from being a Gavra Raba. To claim so is, as I quoted Rabbi Miller, ridiculous.

Good post. Those who claim Chazal (and certainly those after them) were ahead of their time usually are simply unaware of the extent of Roman or Greek learning.

In many ways, things haven't changed much. There are a lot of very intelligent minds in orthodox circles, and plenty of great lawyers. But as a society we are not explorers, nor are we great discoverers of scientific truths. We're book learners, not tinkerers. (Yes, of course, exceptions noted.) Our focus has always been on the spiritual. Chazal were the same. Nearly all of what they knew about the natural sciences was from what they had read from the Romans or Greeks. They weren't ahead of their time in the slightest, it was never their focus. At most you can say some among them preserved a tradition here or there, among the thousands, that was later confirmed to have some scientific basis. You can say the same about the Indians.

The conveyors of the mesorah are indeed those like Rashi and Rambam who have codified and transcribed the oral Torah. Arguably, once the entirety of Torah Sh'baal peh has theoretically been transcribed then no one after can be considered a conveyor of the mesorah. A transmitter of mesorah yes, but no longer a conveyor of mesorah. The difference being giving over something that isn't out there versus giving over something one can look up on one's own. I suppose also that conveyors of mesorah can overlap in conveying perhaps the same idea. (Although, usually everyone has there own unique way of understanding and presenting something)

After hundreds if not thousands posts ' demonstrating' What chazal didn’t know or were wrong about - the same with the Rishonim, the obvious glares at anyone observing this phenomenon. With not ONE post ever mentioning with any bit of awe or reverence the mind-boggling knowledge and insight of the Sages. It's always about what they didn’t know or were incapable of knowing. Imagine writing all the things that Einstein didn't know, yet never mentioning a word about what fabulous knowledge he did have. The reader would be under the impression that Einstein was a total ignoramus. Now imagine someone not in the least familiar with chazal reading post after post about what they didn’t know or couldn't have known. You get the idea....Not that anyone here is ignorant of any chazal or anything....

With not ONE post ever mentioning with any bit of awe or reverence the mind-boggling knowledge and insight of the Sages.

No one here, including RNS, believes that CHaZaL were stupid. We all accept that they were experts in their domain. But we believe that their domain was Torah, not science, nor even natural philosophy (science wasn't really a discipline yet in that era). What RNS does is point this out because people such as RMM love to retroject perfect knowledge of everything on to CHaZaL, when there is simply no evidence that they were particularly knowledgeable even in math, which was well-developed by that time.

You think they are being disparaged as gods, but we think they are being honored as human beings. The truth is that you are Charedi to the core, and your chosen moniker is a lie.

You still don't get it. The point of this site is to explain things from a perspective that isn't charedi Judaism. It's not necessary to talk about how great chazal were because that's not the point of this blog. The premise, at least as I see it, is that RNS is talking to people who are more likely to be familiar with the charedi/literal outlook and not so familiar with the rationalist views. By explaining what chazal said according to those other views, RNS is not claiming that they were ignorant. In certain cases he explains how their statements were misinterpreted, and in other cases it's about how they really couldn't be expected to get it right. If you're convinced chazal were right about everything all the time, this blog isn't going to change your mind, and it's pretty obvious that you're only here to spout against anything RNS says.

The posts aren't there to demonstrate what chazal didn't know. It's to demonstrate that the false and highly exaggerated claims of the charedi world about the chachamim were wrong. You are so out of touch. The biggest danger to the frum world are not those who don't understand chazal, it's those who think they understand them and distort their legacy.

Alas for M_O's observations and deductions, but the reason this blog - and the books, and lectures, and such - does not "focus" so much on what Chazal (or the Rishonim) knew is that this is not a forum for straight up learning Torah. This is a forum for talking about how science, the natural world, animals, etc FIT IN to Torah. And there is a lot of conflict (granted, sometimes less than other times) and often the way to resolve the conflict without losing faith is to say that "It's OK! They didn't need to know this - how could they!" The fact that these lines are almost always accompanied by a dozen disclaimers pointing out that they were still wise and we still respect them etc seems to have passed M_O by.

If M_O or others want a blog where they go through Chazal and the Rishonim systematically and say "Here! They taught us this amazing thing!" then go right ahead. I think many places do this every day. It's called "Learning Torah."

OK OK the response to my suggestion will be that M_O is talking about science topics. So I have an answer for that as well: if there is agreement, then there is nothing to talk about! We know that Chazal were aware that the sun rises in the east and sets in the west. Look! They were astute observers of the natural world!! See how pointless that is? Find a bigger topic, a tricky one, where Chazal/Rishonim actually knew something or predicted it ahead of its time. I'm sure RNS - and the commenting community here - would be glad to celebrate it. (Not to put RNS on the spot - he/we might try to come up with some explanation as to how they would know something out of its time, but if there are to be no such explanations, hooray!)

Gathering from all the recent responses to my comments, it would seem a lesson in Judaism 101 is necessary.

To those of you who subscribe to Rabbinic Judaism and Halachah which is derived from the Talmud, it's quite important to understand who the Rabbis are who's words and dictates you follow. Now they weren't human beings like you and me, for if they were, by the Gemarah's own teachings you would not be required nor should you accept their teachings. Who were they Angels! Now before you get carried away that I'm espousing some chareidi ideology, rest assured I actually quoting a Gemarah in Chagigah "If the Rabbi from whom you learn Torah from is in your eyes like an Angel, from him you should seek Torah" So, regardless of whether they did or didn't know the scientific knowledge sometimes attributed to them, should not detract from viewing them and treating them as Angels.

Considering the above, it would be foolish to negate ANY attributions to Chazal be they Torah or any other discipline for that matter. Can you declare with certainty that chazal were not aware of these attributions to them? However likely or unlikely chazal knew of any given discipline or knowledge - they certainly shouldn't be suspect regarding the things in the Talmud that they actually do claim. Now I'm not saying they knew all science that is currently available to mankind, but why be the fool to think you know what they did or didn't know - consider also you weren't around 2,000+ years ago. Much knowledge about what the Ancient world knew has been lost over this long period of time.

You are either a troll or an example of possibly the biggest problem with extreme Judasim; the elevation of humans to demi-god/angel/saint status. This is heresy 101 - the sin of the eigal ha'zahav was inserting a go-between between us and God! As a jew you should believe in the One and Only God; not a pantheon of other supernatural beings.

Of course the rabbis were normal humans; it is like you have never opened a gemara and seen how they argue and come to conclusions based on logic and wisdom - not supernatural powers.

Read the Rambam's introduction to perek ha'cheilek. I cannot blame you for your ignorance, for even he says the majority of Jews fall under the category of those who taken every word of chazal literally (and you are in that group). The group of Jews, he says, who truly understand and appreciate chazal are those who are able to discern when they are speaking allegorically. Your quote of "the rabbis being like angels" is a prime example of someone misunderstanding chazal. You, and the charedi world in general, take every maamer chazal literally and the result is a misguided perverted view of Judaism, and a major disconnect from the what the chachamim were all about.No they weren't angels. They were in fact human beings. Your ideology is the reason the charedi world is so disconnected from reality and a logical way of life. Hashem yerachem.

"for if they were, by the Gemarah's own teachings you would not be required nor should you accept their teachings"

For someone with so much to say, your ignorance is staggering. Halachah doesn't have to be scientifically accurate. It doesn't even have to be accurate by the standards of the divine-Torah itself. Major Rishonim and Achronim say that R Eliezer was right about תנור עכנאי and the Chachamim weren't. Not only that but the Bas Kol made the Chachamim realize that he was right. Yet it was still forbidden for them to rule against what the majority understood from the Mosaic tradition. If you can go by your understanding against Torah itself, and may not do otherwise, you (Chazal) can certainly go by your understanding against science. See Yoreh Deah 109 that according to some opinions, the majority/רוב allows you to ignore the scientific fact that something is treif.

Read Rashba on meseches brachos, some parts of AGADETAH are to be taken literally some aren't. Note that the reference is only regarding Agadetah. Additionally, in the never ending discoveries of science, science continues to prove itself as a dynamic study with constantly changing variables and 'facts'. Contrast that to the Talmud (after the sealing of the Talmud) which is static and doesn't change. Yes, certain parts were open to interpretation by Rishonim.

I will add, all the attempts to show that chazal are not to be taken literally - have only a limited scope and doesn't apply to every single last teaching of chazal. The burden of proof rests on the one who comes to indicate that s particular chazal shouldn't be taken literally.

Another point: on the idea of chazal being like angels, the concept is generally understood to be referring to the exalted character traits that chazal possessed. As R' Yisrael Salanter said "it is easier to complete the whole Talmud than to correct one character trait" In this sense, chazal were godly and angelic in their positive middos. As to if this angel like behavior carried over to their teachings - I suspect that this is a wide range depending on how fallible or unfallible you are willing to believe chazal were.

Where I personally stand or don't stand in this particular spectrum shouldn't be of relevance here.

My only claim, is to those who do state where they stand that it should meet the following criteria: 1. It be done with the appropriate reverence for chazal 2. Support that a specific chazal shouldn't be taken literally or at face value. To suggest all of the Talmud shouldn't be taken literally is just as obscene as suggesting that the whole Talmud be taken literally.

Indeed, midrashim and aggadeta are not all meant to be taken allegorically. The saying goes: believe all midrashim are false, you're a heretic. believe them all true, you're a fool.I think a strong litmus test as to whether an aggadic statement is literal or not is how it shtims with modern day science or common sense. Trying to dispel scientific facts or historically true events because they don't line up with chazal is moronic, and it is that point at which the sensible thinking Jew will understand chazal were attempting to share a deep insight without it being literal.

Where you stand on that spectrum DOES matter because it shapes the manner in which you see chazal and project their teaching onto the other aspects of the world we live in in which you tend to distort.

"My only claim, is to those who do state where they stand that it should meet the following criteria: 1. It be done with the appropriate reverence for chazal"

People with that claim are often confused. As the rabbi writes, http://zootorah.com/controversy/scienceresponse.htmlin response to the "tone" complaint,"Charge #4: The tone ... is wrong; the author writes without the proper reverence for Torah sages."My Response: I have repeatedly requested examples of this and only ever received a very minor example that was easily changed. After contemplation and investigation, it appears that when people speak about "tone" (which is usually understood to mean "phraseology") they are really referring to the approach (methodology). For example, when someone claims that I did not write about the Sages with sufficient respect, they usually mean that I did not conclude that they were correct in certain cases and accepted the conclusions of modern science instead .... In any case, complaints about phraseology are highly subjective; standards of propriety vary greatly between different cultures and communities. Many of those who benefited the most from the books specifically appreciated their forthright tone, while some found them overly deferential to traditional authorities!"

So make up your mind. What phraseology won't you complain about? How about, "camel feet aren't the way Chazal/Rashi/Rashbam/etc. describe them"? Or is that also not good enough unless Chazal/Rashi/Rashbam/etc. are correct?

It's also readily apparent that you have zilch experience teaching a mixed crowd that includes the semi-committed. You always have to have a feel for not pushing them beyond where they can be holding. You never say anything that will make some say you are worshiping Chazal. Did you notice how poorly your "angels" idea was received right here? The way to go is just teach the subject, adjusting it with common sense.

Please see this with my previous 3 comments. I hope they settle all the loose ends.

And as for Judaism 101, it seems that you need remediation in Reading Comprehension 101. Every single statement of R Slifkin and by most of the learned commenters here clearly show awareness of and respect for the wisdom and knowledge of Chazal and Rishonim. The plentiful disclaimers, the pointing out that we don't feel that it's an insult to say that someone doesn't know something, etc. After all, the WHOLE POINT of the blog - or Rationalist Judaism as a whole - even existing IS THAT VERY FACT! If we didn't care, if the knowledge of modern science made us throw religion away, why would R Slifkin write book and after book and spend so much time trying to understand one in light of the other? We are trying to be frum in a scientific world!

(Of course I agree with the comments above about Chazal being real people, but this is a) no less true and b) works better in M_O's worldview.)

MO, “my custom is to commence drinking 30 days before the holiday.....” You don’t say which holliday.The silly buffoonery that passes for logic suggests that the onset of your inebriation began with the 30 days before the holiday of last year’s Shavuot. That might account for broken logic and ineptitude in your clumsy argumentation.Try limiting your boozing to 7 days before Purim (THIS year’s Purim) and you might present a cogent argument. However sobriety might not act in your best interest. A lucid state of mind would not deliver the drivel that oozes from you.

Certainly having a sense of humor raises the esteem one can rouse in others, so points for that.

But on the specific issue of "Religion by definition can't support tolerance or Rationalism" - wow!! Which religion are you talking about? Evangelism? Radical Islam? 'coz it ain't Judaism.

We invented tolerance - allowing for the ger toshav who did not have to convert. While there were periods of Judaic proselytizing throughout the ages (resulting in Herod's father being brought into the fold, and we see where THAT went), generally we do NOT insist that everyone be like us. After all, where would we get our Shabbos goys?

And Rationalism? I couldn't match what others here could say, but are we not supposed to think? To use logic? Perhaps we have to submit to the Sanhedrin when they say that left is right and right is left, but we shouldn't convince ourselves of the empiric fact that that is so!

Of course, if the whole post was a Purim joke, then whew! Joke's on me.

I will be expecting lots of M'Shloach manos from all my 'good friends' here....Love you all, hope everyone understand that these discussions are purely philosophical in nature and not personal......Maybe one day you will find out who this guy masquerading as a 'chareidi' really is.....

Does Rambam say that Chazal knew it was irrational? Here's an online version of his commentary on Eruvin 1:15 and I also compared the text in the Mossad Harav Kook version and I'm not seeing it. https://www.sefaria.org.il/Rambam_on_Mishnah_Eruvin.1.5.1?lang=bi

He doesn't. The phrase "אבל הוא בטבעי זה הדבר בלי ידוע ואין במציאותו שיושג" can be interpreted to mean that pi is not rational. (An exact value for pi would consist of a rational number aka a fraction. If it is impossible to find such a number, then pi is irrational by definition). However, he states this as something well known the educated and only denied by foolish people. He doesn't claim that he or Chazal had any special knowledge. (Also, he didn't actually know that it was irrational, because he had no proof of this, and knowledge in math consists of having a proof.)

The whole thing is foolish. The only possibly notable thing is that Rambam is first or one of the first to conjecture the irrationality of pi so explicitly or emphatically.

"Since it can never be grasped without using an approximation they [Chazal] used a rough estimate."He states that the reason Chazal used a rough estimate is because pi can never be expressed precisely.

It seems to me that רמב’’ם is claiming that חז’’ל chose to use the חשבון הגדול because they knew that pi is irrational.

Yes, he claims that all knowledgeable people know that pi is irrational. That is why the great geometers came up with the 22/7 estimate. Then he uses that to justify Chazal using a very crude estimate of 3.

Rav Slifkin: The next time you post this or something like it, you may want to include links to videos with proofs that pi is irrational, like https://www.youtube.com/watch?v=Lk_QF_hcM8A and https://www.youtube.com/watch?v=KcjGe5a7Lwg

More intriguing would be if he would address why the Rambam considered pi irrational. The Rambam was an accomplished mathemation. Also who were those he referred to as idiots for not realizing pi is irrational?

Rambam was very intelligent and well-educated, but not an accomplished mathematician. Most likely, he considered pi probably to be irrational for the same reason everyone else did: no one could construct a rational equal to pi and the ancients had proved long before Rambam that some numbers (like the square root of 2) are irrational. Rambam often made very definitive statements about things that he conjectured to be true and insulting remarks about those whom he considered uneducated. He made the same kind of assertions about spontaneous generation and said the same insulting things about those who didn't believe in spontaneous generation.

See R' Berel Wein on the Rambam. The Rambam was irrational as is anyone who insists on explaining everything rationally - including explaining the irrational.

Religion by definition is irrational, since by definition religion is based on a system of beliefs - now believing in something that is not necessarily a scientifically provable fact, well that's irrational.

Why does it matter if Chazal or the Rambam knew any particular scientific or mathematical fact? First of all, at least some of what they thought they knew has either been found to be untrue, simplistic, or incomplete, just as in 1000 years, what we think of as scientific and mathematical facts might found to be less than 100% correct. That is the nature of science and math -- they keep improving on what we know at any particular time. However, at a certain time, wherever we are is the best we can do at the moment.

But I still don't care if they knew that PI is irrational. That isn't what I, or I think anyone, should look to them for. Just like I don't ask my doctor how to fix a running toilet, I would not ask my rabbi for help with my physics homework. Doesn't at all mean I don't hold my rabbi in the highest regard and have great respect for his knowledge and wisdom. But not when it comes to physics because he clearly does not know anything about it when compared to his Torah knowledge and wisdom. And I think if I told him this, he would be the least bit insulted.

So Chazal got PI wrong. Only if you claim that they are mathematical authorities, which seems unreasonable and unwarranted, would one have a problem if they got it wrong. It does mean that everything they say is wrong, just those things that they have no special knowledge or expertise in they might get wrong. Isn't that OK?

This is not a post about why it is wrong to have illegal minyanim in basements. Other people have already written about that with great ...

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